Last Friday 18th Jan, EMA airport was closed due to snow. I was waiting at AGP for my flight home with FR at 2055. It was clear that the incoming FR flight was never going to get to depart from EMA as my wife told me the weather was getting worse. So why didn't they declare the flight as cancelled? Every other EMA operator had done so. EMA departures still show the outbound flight as 'Final Boarding'. In the end, myself and 4 other PAX took a risk and jumped onto a flight to STN and got a taxi back to EMA (£210 between us) and we got home 5 hours late. But at least we got home. What happened to the other 150 PAX trying to get to EMA I don't know.
Is there some mis-communication between the airport and the airline that prevents us simple PAX from knowing what is going on?

I can't speak for your specific situation when flights get cancelled here in the US the main driver for that is flow rates wanted by the FAA. In cases where forecasted weather is beyond that which it is safe to fly, the amount of time that weather is to last as well as the impact to the rest of the system has to be taken into account. If for example waiting it out to get that plane to a certain city so that other flights are not cancelled as well can be accomplished. There are so many factors, the weather is just one component in determinimg that.

When the weather (origin, destination, alternate) is below minimum and not expected to improve within a reasonable amount of time. If sitting at a hub it is more likely to cancel if running this flight will severely impact down line flights. Think canceling one flight to put the 5 in the rest of he day back on time instead of 3 hours delay each.

If waiting for weather to improve the crew would time out.

If there is simply no way to get somewhere safely.

If the weather is bad enough the airplane could not handle it.

That's all I can think of. It's almost always a combination of weather, machine, human, and time factors. Weather alone usually don't get flights canceled.